We know that:
[tex] PA = PB = 15 [/tex]
Using the Pythagorean theorem in the right triangle on the right we have:
[tex] CP ^ 2 = CB ^ 2-PB ^ 2 [/tex]
Then, again using the Pythagorean theorem in the right triangle on the left we have:
[tex] CA ^ 2 = CP ^ 2 + PB ^ 2 [/tex]
Substituting values:
[tex] CA ^ 2 = (CB ^ 2-PB ^ 2) + PB ^ 2 [/tex]
Rewriting the expression:
[tex] CA ^ 2 = CB ^ 2 [/tex]
[tex] CA = CB [/tex]
[tex] CA = 15 [/tex]
Answer:
The value of CA is given by:
[tex] CA = 15 [/tex]
